Anand clinched the 12-game match in the 57 moves with the black pieces to claim his title with a score of 6.5-5.5.
The 40-year-old Indian, who won world title for the first time in 2000, lost the first game but had his match winning moment when Topalov blundered on his 31st and 32nd moves.
Anand went on to win the second and third game after losing the first game.
Anand claimed the world title in 2000 and held on to it till 2002. He became World champion in 2007, which he retained in 2008 after defeating challenger Vladimir Kramnik.
He had travel more than 40 hours by road to reach the venue as the flights in Europe were suspended due to the volcanic ash cloud from Iceland.